OptMATH: A Scalable Bidirectional Data Synthesis Framework for Optimization Modeling

2025/02/16 by Hongliang Lü, Lu, Hongliang, Y.C. Wu +7 · 10 citations
Computer Science · Decision Sciences · #Artificial Intelligence (cs.AI) #Embedded Systems Design Techniques #FOS: Computer and information sciences #Machine Learning (cs.LG) #Parallel Computing and Optimization Techniques #Simulation Techniques and Applications

paper · pdf · doi:10.48550/arxiv.2502.11102

openalex publication_date 2025/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Despite the rapid development of large language models (LLMs), a fundamental challenge persists: the lack of high-quality optimization modeling datasets hampers LLMs' robust modeling of practical optimization problems from natural language descriptions (NL). This data scarcity also contributes to the generalization difficulties experienced by learning-based methods. To address these challenges, we propose a scalable framework for synthesizing a high-quality dataset, named OptMATH. Starting from curated seed data with mathematical formulations (MF), this framework automatically generates problem data (PD) with controllable complexity. Then, a back-translation step is employed to obtain NL. To verify the correspondence between the NL and the PD, a forward modeling step followed by rejection sampling is used. The accepted pairs constitute the training part of OptMATH. Then a collection of rejected pairs is identified and further filtered. This collection serves as a new benchmark for optimization modeling, containing difficult instances whose lengths are much longer than these of NL4OPT and MAMO. Through extensive experiments, we demonstrate that models of various sizes (0.5B-32B parameters) trained on OptMATH achieve superior results on multiple modeling benchmarks, thereby validating the effectiveness and scalability of our approach. Our dataset is publicly available at https://github.com/AuroraLHL/OptMATH.

Cited by

• Solver-Independent Automated Problem Formulation via LLMs for High-Cost Simulation-Driven Design
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• AlphaOPT: Formulating Optimization Programs with Self-Improving LLM Experience Library
• CALM Before the STORM: Unlocking Native Reasoning for Optimization Modeling
• REG: A Regularization Optimizer for Robust Training Dynamics
• OptiMind: Teaching LLMs to Think Like Optimization Experts
• OptGraph: Large Language Models Enhanced Evolutionary Optimization Via Graph Retrieval-Augmented Generation
• Large Language Models in Operations Research: Methods, Applications, and Challenges
• Toward a Trustworthy Optimization Modeling Agent via Verifiable Synthetic Data Generation
• Auto-Formulating Dynamic Programming Problems with Large Language Models

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